Some results on Horadam quaternions

Elif Tan; Ho Hon Leung

doi:10.1016/j.chaos.2020.109961

Some results on Horadam quaternions

Elif Tan, Ho Hon Leung

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

8 Citations (Scopus)

Abstract

In this work, we present some matrix representations associated with the Horadam quaternions which are defined by W_n=w_n+w_n+1i+w_n+2j+w_n+3k, where the components are taken from the Horadam sequence {w_n}. We derive many identities related to them by using the matrix technique which is more practical. Since various well-known Fibonacci-type quaternion matrices are special cases of Horadam quaternion matrices, we have a unified way of dealing with many special quaternion sequences in the literature. As an application, we derive some binomial-sum identities.

Original language	English
Article number	109961
Journal	Chaos, Solitons and Fractals
Volume	138
DOIs	https://doi.org/10.1016/j.chaos.2020.109961
Publication status	Published - Sept 2020

Keywords

Fibonacci quaternions
Horadam quaternions
Matrix method
Quaternions

ASJC Scopus subject areas

Statistical and Nonlinear Physics
General Mathematics
General Physics and Astronomy
Applied Mathematics

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10.1016/j.chaos.2020.109961

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title = "Some results on Horadam quaternions",

abstract = "In this work, we present some matrix representations associated with the Horadam quaternions which are defined by Wn=wn+wn+1i+wn+2j+wn+3k, where the components are taken from the Horadam sequence {wn}. We derive many identities related to them by using the matrix technique which is more practical. Since various well-known Fibonacci-type quaternion matrices are special cases of Horadam quaternion matrices, we have a unified way of dealing with many special quaternion sequences in the literature. As an application, we derive some binomial-sum identities.",

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AU - Leung, Ho Hon

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AB - In this work, we present some matrix representations associated with the Horadam quaternions which are defined by Wn=wn+wn+1i+wn+2j+wn+3k, where the components are taken from the Horadam sequence {wn}. We derive many identities related to them by using the matrix technique which is more practical. Since various well-known Fibonacci-type quaternion matrices are special cases of Horadam quaternion matrices, we have a unified way of dealing with many special quaternion sequences in the literature. As an application, we derive some binomial-sum identities.

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KW - Matrix method

KW - Quaternions

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Some results on Horadam quaternions

Abstract

Keywords

ASJC Scopus subject areas

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